This is common in my field, physics, to the extent that at least one publisher has an explicit policy encouraging it:
The submission of an expanded version of a PRL to a topical Physical Review journal is an established practice that provides readers with easier access to important additional information. If authors simultaneously submit a Letter to PRL and a regular paper to one of the Physical Review journals, the two manuscripts are then reviewed coherently, typically by the same reviewers. If both papers receive favorable reviews, we aim to publish them at the same time, unless this leads to undue delay for one of them. We also ensure that the paper and the Letter cite each other.
Submitting a joint publication couldn’t be easier. Simply alert the editors by mentioning the companion papers in your cover letter.
For example, consider the case when you have come up with a great new method to calculate something. Then the letter would tend to introduce the method, and show results from an example application or two. (Naturally, these examples are usually the ones with the most impressive or surprising results.) The full-length article wouldn't so much repeat what was stated in the letter as it would extend it. It might provide more details and justification, applying the method to a wider set of systems, and showing some less central conclusions. The idea is that it should still be a different paper, but there is less need for the letter to be fully self-contained.
That said, it's even more common to first write up the more "exciting" results, submit that as a self-contained letter, and then submit a more extensive follow-up as a regular article later. I don't know how universal either practice is, so you might want to check with an advisor, or mentor, or colleague to figure out if this is an accepted practice in your field, and what the expectations would be.